This invention is in the field of analyzing rock samples to determine petrophysical properties.
As is fundamental in the oil and gas industry, the knowledge of the properties of the material of subsurface rock formations is important for assessing hydrocarbon reservoirs in the earth, and for formulating a development strategy regarding those reservoirs. A wide variety of tools and techniques for obtaining this information are well known in the art, and range from seismic data analysis, obtaining and analyzing core samples from the formations of interest, and various indirect measurements of the earth that are obtained during the drilling process.
A common technique for analyzing a sub-surface formation is resistivity logging along a borehole into the formation. Conventional resistivity logging measures the electrical response of the formation surrounding the borehole, typically to derive a value referred to as the “formation factor”, which is the ratio of the resistivity of the fluid-bearing rock to the resistivity of the fluid itself. According to the well-known Archie's Relation, the formation factor is solely a function of the pore geometry of the rock, and can be correlated to porosity by way of an exponent referred to as the cementation exponent. As a result, analysis of a conventional resistivity log can provide important information regarding the porosity or water saturation of the formation of interest. In addition, resistivity logs in combination with the appropriate rock physics interpretation can provide insight into the permeability of the formation.
While Archie's Relation is commonly used to interpret electrical response from logs and from core samples, it was originally formulated based on a series of experimental measurements. It has been observed, however, that Archie's Relation is valid only for petrophysically simple rock formations, examples of which include clean sands. It has been further observed that Archie's Relation does not hold for shaly sands, namely sands containing clay minerals. A conventional approach for analyzing resistivity logs from shaly sands is referred to in the art as the Waxman-Smits Method. However, this approach is somewhat limited in practice, as it requires knowledge of the cation exchange capacity of the clay mineral in the shaly sand in order to correlate resistivity with water saturation and porosity.
The presence of clay within a rock sample has been observed to complicate the interpretation of electrical data obtained from logs and core samples. One reason for this is that the electrical properties of clay minerals (also referred to herein as “clays”) are not well understood. In this regard, the interpretation of electrical properties (and associated properties such as cation exchange capacity) of clays as measured in the laboratory has proven difficult. This complicated interpretation of electrical data from clays also arises from the structure of typical clays being on the “nanoscale”, which is much smaller than that of sands and which renders clays less amenable to atomic resolution experiments and analysis. In addition, the crystalline structure of clay minerals is often quite irregular, such as consisting of thin plates that are not oriented parallel to one another, with oddly-shaped boundaries and unusually-shaped pores. Furthermore, impurities that are often present in clays, particularly at external surfaces of the plates, can displace other atoms by substitution and change the charge distribution in the clay material. In general, these complexities of the nanoscale crystal size, the disorder of crystals and plates, and the complex composition of clay minerals render the direct measurement of petrophysical properties on clays very difficult.
Direct numerical simulation of material properties from digital images of rock is a recent technology for determining the material properties of rock samples. According to this approach, an X-ray tomographic image is taken of a rock sample to produce a digital image volume representative of that sample. A computational experiment is then applied to the digital image volume to simulate the physical mechanisms from which the physical properties of the rock can be measured. Properties of the rock such as porosity, absolute permeability, relative permeability, formation factor, elastic moduli, and the like can be determined using direct numerical simulation.
Specifically, direct numerical simulation of electrical properties from digital images of rock, is accomplished by approximating or solving relevant electrical equations such as the Laplace equation with variable coefficients and relevant boundary conditions. This approach assumes, however, that the electrical properties of constituent materials within the rock are known. For instance, solid grains (e.g., quartz) can be considered as nonconducting, clay fractions as partially conducting, and pore fluids such as brine as the most conducting phase in the simulation. While this assignment of conducting properties is well understood for solid grains and pore fluids, a physical basis for the assignment of the conductive properties to clays has not been established. As such, the use of assumed values for clay conductivity leads to uncertainties in conventional simulations of the electrical response of clay-bearing sands.
By way of further background, molecular dynamics (“MD”) simulation refers to a computational method of describing the evolution, over time, of a finite molecular or atomic system, based on an approximate expression (i.e., a “force field”) that determines the potential energy experienced by each atom in the system. In a conventional MD simulation, data such as coordinates, velocities, and forces for each atom under the force field are stored at periodic time intervals. These data are then used to calculate instantaneous and time-averaged properties, such as atomic or molecular trajectories, atomic or molecular density profiles in either one or two dimensions), interatomic structure (e.g., a radial distribution function), diffusion coefficients, vibrational structure, and the like.